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Title: Mathematical anarchism Author: Evo Date: 2020 Language: en Topics: complexity theory, systems theory, science, the future, utopia, anarchist analysis, self-organization Source: Retrieved on 2020-07-31 from https://mathematicalanarchism.files.wordpress.com/2020/03/bookleteng.pdf
All-over I search the answer to three questions in this booklet, which
are about respectively the what, the origin and the future. The
what-question is about what hierarchy on the one hand, and freedom on
the other, is. The second question is how hierarchy can emerge, while
the last, most interesting question deals with how we can move away from
this and create a free society.
This by aiming to go to the root of the matter and dissect some
underlying concepts and mechanisms.
This booklet is based on my PhD âSelf-organization versus hierarchical
organization â a mathematical investigation of the anarchist philosophy
of social organizationâ
Any feedback â comments, questions, ideas, errors, remarks,âŠ? Or want to
see more?
mathematicalanarchism.wordpress.com
---
Okay, how did I come to this idea of combining anarchism with
mathematics?
To me it was to some extent a natural combination, as Iâve always been
passionate about both mathematics and anarchism. I have a problem with
authority, with power, and with everything that restricts my freedom or
coerces me. And thus I want to find out how we can create a world where
no (or less) coercion is present.
But by thinking about this, I came to the conclusion that these concepts
are less easy to define than I thought. Also because in todayâs world,
coercion is often less explicitly visibly than before, where there was a
clear hierarchical structure with, for example, a king on the top of the
pyramid. Today the source of a perceived lack of freedom is less easy to
find. For example, technology creates alienation and addiction: we have
thousands of friends in Facebook, but lack true, deep connection. We
work nine-to-five in a boring job to make a living. Nobody who forces us
to do so, and still we have the feeling our lives arenât in our own
hands.
And to understand these things better, I turn to math, or wiskunde in
Dutch, which you could translate literally as the art of erasure. To me,
math is about going to the essence, to distil common mechanisms,
relevant to your question, out of a bunch of phenomenons. By simplifying
to basic concepts, you can go further: you can let your imagination go
wild on them, and construct things which would be way to complicated
when starting from the messy reality. And these imagined concepts can be
brought back to reality, to make dreams come true there. Radically going
to the root of things, so that freedom can grow wildly.
But you donât have to be a math whiz to understand this booklet. Math is
more the underlying way of thinking, as in how I explained it above.
With my mathematical, abstract, systematic brain I took a look at
anarchist ideas, which resulted in new notions which are hopefully also
interesting for the non-mathematician (and which are not always
mathematical).
Iâve put specific mathematical elaboration in special Yeah, math! -boxes
â these are not necessary to understand the whole and can thus be
skipped. And then there are the A story: -boxes, in which I give
examples of just seen concepts.
The footnotes refer to a work on which that part is based, no need to
stop your reading unless you want to check out more.
A common thread throughout this booklet is the difference between a
hierarchical structure and different connected cycles. After explaining
this difference, Iâll explain how it corresponds with a functional
difference between hierarchy, power, coercion, external coercion on the
one hand, and freedom, autonomy, internal control on the other. After
that, I dive deeper into the structural with other possible
representations of (non-) hierarchical structures, and explain why they
are just different depictions of one and the same concept.
Then we discuss how a higher-order controller can emerge. To finally
suggest some ideas on how we can evolve to a free society, more alike to
the living, cyclical of an ecosystem, and not based on hierarchical,
authoritarian state structures.
But not all my ideas can be spanned under this common thread. Precisely
because they do not form a hierarchical structure with one main idea and
different subordinate sub-ideas. The ideas link between each other, they
can form cycles, where one idea strengthens another, but the last idea
in the end also supports the original idea. That may make it difficult
to follow (since to understand one part completely, you should actually
already have read a further part), but it also makes that you can read
in any order you want. So maybe you are mainly interested in how to
increase your freedom, go and jump then directly to that chapter.
The differences between a hierarchical and a cyclical structure can be
illustrated in following figure:
[]
One of the things that stand out in the left, hierarchical figure, is
that there is an anti-symmetry: an arrow always goes from a âtopâ
element to a âbottomâ element, never in the other direction. This
happens directly â there can only be an arrow between two elements in
one direction â as well as indirectly â if an element A is connected
through different arrows with an element B, there can be no arrow from B
to A. In the alternative, if this does happen, they are automatically
cycles: through different arrows we in the end arrive back at the
original element.
Another property from the hierarchical figure is that there is maximal
one arrow arriving at each element, while often different arrows depart
from it. On the other hand, in the right, non-hierarchical figure arrows
from different elements can arrive at one element.
These two properties of a hierarchy cause a tree structure. We can prove
that there is only one top element if these two properties are valid and
the structure is finite.
In the following I will describe the left situation as hierarchy, while
Iâll talk about (entangled) cycles for the right situation (where I thus
assume that there also arrive different arrows).
---
Yeah, math!
[]
[]
---
[]
All of this probably sound abstract, what does this entail concretely?
The easiest to imagine, is to view these arrows as influence, as a
cause-effect relation.
Anti-symmetry then means that influence only goes in one direction,
whatâs sometimes defined as power-over: someone has influence over you
while you donât have influence back. A power relation thus, but
different from power-to, the power to accomplish things.
If moreover you can maximally have one influence, you can be completely
determined by that influence.
If on the contrary there are multiple inputs, you can form a creative
combination of them, more than the sum of the inputs â thus a sign of a
lack of hierarchy.
---
A story:
Nurture-vs-nature debate on gender: neither, but self-creation
An often heated discussion, especially on the topic of gender, is
whether we are influenced by nature or nurture: are men and women
biologically determined to act differently or is this conditioned by
society? One of the reasons I think this discussion is so heated, is
because both parties feel their free will is denied. The ones say you
should take certain roles because of your biology. The others claim we
are just a product of culture, independent of our own make-up.
Self-creation is a way out of this deadlock: we have created ourselves
from both biological and cultural influences. We can partly decide
ourselves who we want to be and what we want to do and thus have a free
will. Though you shouldnât deny that culture thus influence you, just
like you have a certain biological base (but one more diverse than a
simple X or Y chromosome).
To me, transgenders are proof that there is something more at play than
nature or nurture. Because both your biology as society can say that you
are, for example, a girl, and still you can know that you are a boy (or
something else). It is not that it is merely a choice: a complex system
has formed, which has its own identity that is not merely determined by
the influences that have created it.
---
On a fundamental level, cycles make that there can be self-causation,
where we can cause our own existence, inputs are getting created from
outputs. Sure, we cannot just pop out from nowhere, but once we are
there, we can maintain ourselves, and set and follow our own goals. We
are autonomous and can create ourselves. A fancy word for this concept
is autopoiesis (auto=self, poiesis=creation), which we, for example,
assess in all living beings [1].
Note that usually there is not one isolated cycle, but different
entangled cycles. Where there can thus be different influences working
on one element, which can give a unique, unpredictable consequence,
making the system dynamic. The different cycles form a complex system,
where we unravel two properties linked with autopoiesis. The first is
that the system can maintain itself: everything that is used by the
system, is produced by the system in at least as much. Secondly, the
system is closed: everything that gets produced, was already part of the
system.
---
Yeah, math! [2]
[]
---
But in practice there are still influences from the environment. But in
an autonomous system, the system itself decides what to do with those
influences and can decide its path independent of these influences.
This is in general what cybernetics describes as control: a feedback
cycle where a controller does certain actions to get its input closer to
its goal â see following figure. I will often have such scheme in mind
when speaking about an agent or an autonomous system.
[]
To investigate the effect of different influences on a result, I
differentiate internal and external control. Internal control is if a
change of your influence can cause a change in the result (we
specifically mean the result important for you; this typically relates
to your goals and/or the inputs you will receive). While there is
external control if an external influence brings a change in the result.
In itself the one doesnât exclude the other, but do be autonomous we
mainly want internal control: we want to be able to decide our own path.
Take as example the external influence of the wind. Most objects simply
fly along the wind and thus have little internal control. But a good
cord dancer can continue to follow his path on the cord, despite the
wind bringing him out of balance, by doing counter movements. A sailor
can even use the wind to go in any direction, even against the wind (by
zigzag). Still the wind just keeps on blowing, and we donât change its
direction by our deeds. But the cord dancer can also lose its
equilibrium, in which case it no longer has internal control.
---
A story:
Parkour
Parkour is an example where internal control is increased without
changing the environment. In parkour, walls and everything found in an
often urban environment become challenges which can be jumped and
climbed over, on and under. Parkour is more than a sport, it is a
philosophy.
The environment doesnât change, but parkour does change the perception
of the environment. Walls are no longer obstructions that block your
way, but challenges to do new movements. Parkour is about creating your
own path instead of following a predetermined path. This philosophy can
be applied more broadly than literally. Obstacles that you encounter in
life can be seen as challenges, chances for growth and gratification.
The world becomes a playground. Your world thus no longer looks the same
after doing parkour.
Of course you still want an interesting world, thus not a plain without
hindrances or one with insurmountable walls. But even there the art of
parkour is to nevertheless find challenges.
Parkour shows that external control isnât necessary to deviate from the
predetermined path.
You could also look at it from the perspective of your influence on the
environment: how hard do you want to change the environment to have
control? With internal control the focus is then on your own situation,
while with external control you mainly want control over your
environment. In the example of the wind: we could develop ways to go to
the wanted direction independent of the direction of the wind (internal
control), or we could try to control the direction of the wind (external
control).
---
Yeah, math!
[]
[]
---
[] Two interpretations of freedom
Roughly, freedom is understood in two distinct ways. Underlying in the
first conception is the cycles: freedom is here linked with autonomy,
self-creation. Here freedom can only be taken or created by yourself.
Freedom here means spawning your own possibilities, to break out of
existing constraints. It is a conscious decision, and not something you
can simply get. The focus can be more on the negation of coercion and
constraint, or more on the positive of developing and actualizing
yourself.
Another perspective starts from a hierarchical thinking: here freedom is
something that can be given from outside, a right. This is typically the
freedom in a democracy, think about freedom of speech, freedom of
association, ⊠In general, this is the freedom to choose from already
pre-given options. This is the capitalistic freedom where you can choose
the colour of your coffee machine.
What is it then exactly that hinders this freedom? Therein I
differentiate two concepts, which are often used interchangeably:
coercion and constraint. Coercion is if you are obliged to do something
you do not really want to do. Constraint is what limits possibilities.
Often this is viewed mathematically as a precondition, something that
reduced a set (of solutions). Actually, there are always constraints,
otherwise we would simply float around in a random soup of loose
particles â it makes us exist at all. In short, it makes the world
interesting.
Constraints arenât necessarily coercive. Moreover, as soon as we choose
for ourselves to go into a certain direction, we put a constraint on
ourselves. And exactly this possibility could be seen as why we are
autonomous, free individuals.
[]
On the other hand, coercion can increase your options. You could be
forced to do something you would otherwise never do, cancelling some
constraints. A soldier could for example be sent to the other side of
the world and thus discover all kinds of countries and experiences he
would otherwise never have encountered.
[]
Coercion sounds like a better concept to name the lack of freedom we
want to speak about. Only: it is not that easy to decide when someone is
coerced. The âwillâ or goals of someone canât be assessed directly, we
canât look inside someoneâs head. Therefore, the will (or a goal) is
often defined based on what you do: if you put a lot of effort into
achieving a certain situation, it is assumed that situation is a goal of
you. But if you assume what you do is a direct consequence of what you
want, then you can impossibly do something you do not want. And then
coercion is an impossibility.
These philosophical reflections in the difficulty of knowing when
someone is coerced, translate to practice. Addiction is a typical
example of what is at play here: for the outside world a person can do
things that are not the best for him, and thus be addicted, while the
person himself doesnât see the problem (or hides it for herself), and
still sees it as something positive. Such a mechanism can be recognized
more broadly than purely in the addiction to drugs.
Often there is a dependence â one is dependent of an outside source to
provide for certain needs. A dependence makes you vulnerable for
coercion, because that external source can expect certain things in
exchange for the demands you need. But in itself, the input from an
external source can also be wanted. In general, there is determination â
an external source decides your output (/input) instead of yourself.
[]
Consequences determination
We can now discuss the structural side of hierarchy.
We already discussed a first representation in the beginning, remember
this figure:
[]
Here we have a structure with arrows, which is why we speak about
directed networks. In this case, a hierarchy means anti-symmetry and
maximally one influence per element, while a non-hierarchical structure
exists out of cycles where elements can have multiple influences.
Of course in practice these structures are in between these two
extremes. We can thus look to how hierarchical a certain structure is:
how many elements are part of a cycle, how much influence do these
cycles have on the overall structure, and whether multiple arrows leave
or arrive in an element[3].
Other mathematical types in which we can investigate hierarchy, are sets
and undirected networks.
If we look to sets, hierarchy is presented by a big set with smaller
sets in it, where every smaller set contains in itself even smaller
sets, and so on. Think about a country with several regions, where every
region contains different communes, and every commune exists out of
several households. Typically is that every group has someone as head
who represents the group: the prime minister, the first minister of the
regions, the mayor, the householder. In a non-hierarchical structure on
the other hand, there are different groups that overlap, none containing
the other â you are, for example, in a sport club, you have a group of
friends from the past, you have a group of colleagues, a family,⊠Some
people from your sport club will, for example, also be in your group of
friends, but both contain persons that are not in the other group.
In fact this is just another way of representing structures, and
hierarchy here is the same as hierarchy in the directed networks of
before. We can consider that a set âinfluencesâ another set if there is
overlap between them, and the first has elements which are not in the
second. Then we can define a link from the one set to another. In the
hierarchical case we see that the bigger set influences the smaller sets
under it, and we thus get a tree structure. In the non-hierarchical case
there is mutual influence between overlapping sets, and thus cycles.
[]
Sets are actually a way of categorizing, because we choose which
elements form a set, and which donât. This difference in categorizing
leads to a different way of thinking. Some like to focus on a
universality; they prefer one big all-encompassing something, that can
be divided in several smaller elements. A hierarchical way of making
sets. In science, this is, for example, the idea that you need to have
one big thesis split and worked out into several smaller ideas. In
political struggle, it is the idea that one struggle is the most
important (for example the economical struggle), and that other
oppressions are the consequence of that one oppression (for example that
sexism, racism,⊠is only an effect of economical oppression). This idea
is often prevalent in Marxist circles. Another way of thinking focuses
on local coherence: ideas or elements can be coherent between themselves
without forming an all-encompassing whole. Exactly because there is more
interdependence than in a hierarchical structure where elements are only
connected through top elements, this creates more coherence. This is for
example the idea that different struggles can reinforce each other.
But there can also be hierarchy while the relation looks symmetrically
locally, in the way in which this relation is embedded in the bigger
network. Thatâs why it can also be interesting to look to undirected
networks. The basic idea here is that in a hierarchy, the âlowerâ
elements are only connected with each other through a âhigherâ element.
In a hierarchical network elements with little connections cluster
together (they do not have acquaintances their neighbours do not have),
while elements with a lot of connections connect different clusters.
In fact we can bring this back to sets, by looking to the sets of
neighbours of elements. In a hierarchy the sets formed by the least
connected elements are the basic clusters. Different clusters form a
bigger cluster, connected through an element with more links. These
different bigger clusters tangle together into an even bigger cluster.
Until we have one big cluster of all elements, all connected through the
top element. This thus corresponds with our representation of hierarchy
as sets. In a non-hierarchical structure on the other hand, every
element has acquaintances which its neighbour doesnât have. This
corresponds to overlapping sets of acquaintances. The way we represented
non-hierarchical structures.
The three ways in which we defined hierarchy, thus correspond with each
other. These are hence three different ways to represent the same
concept.
---
Yeah, math! [4]
[]
[]
---
This last way of representation can also give inspiration of how a
structure can change. If elements of different clusters directly
connect, they bypass the top element, getting different input than that
from the top element, hence making the structure less hierarchical.
To summarize, Iâve analysed hierarchy here both functionally and
structurally and noticed that there is an accordance between the two. In
a hierarchy there is anti-symmetry and every element has maximally one
influence. This anti-symmetry causes a power-over relation: there is
influence on an element without that element having influence back. Such
a relation causes dependence, making one vulnerable for coercion, where
you are forced to do something you do not want to do. Coercion differs
from constraint, the limitation of possibilities. Having one influence
makes that you can be determined by this influence. Internal and/or
external control settles whether the output is determined by you and/or
an external source.
[]
But how do certain constellations emerge? This is important to know, so
that we can recognize and avoid the mechanisms that bear hierarchy.
[]
Self-organization can be defined as local interactions that generate a
global pattern. In general this happens by coordination between elements
(for example individuals): they work together to reach their personal
goals better. The purpose is pretty clear, together you can do more than
alone. Coordination can happen by alignment: elements adapt to the
direction of their neighbours, so that all elements point in the same
direction â take as example a magnet. In this way friction is avoided,
where elements counteract each other. Synergy happens when collaborating
delivers more than the sum of the parts. Elements donât need to have the
same goals for coordination â they can also advance each otherâs goals.
Concrete methods for coordination without top-down control will be
discussed in the next chapter (âRooting out hierarchyâ).
[]
This global pattern emerging from coordination can however become a
global goal. And a goal entails a control-mechanism: actions are done to
bring the situation closer to that goal. A higher-order system thus
originates, an organism with its own goals. This is how we emerged from
different cells, but this is also how organisations come into being.
This higher-order system starts to exist on its own, only interested in
reaching its own goals. The personal goals of the elements that
originally formed this higher goal, are pushed to the background and can
thus become more and more disconnected. The elements are purely in
function of this higher goal (from the point of view of the larger
system). Maybe the larger system can do things which are good for the
elements, but this happens purely as a coincidence. For example, we
donât care that much about our individual cells, and will in certain
circumstances even destroy them if it is better for our organism as a
whole.
If we look to organisations, we see that they are often formed around a
common goal. However, the longer the organization exists, the more the
organization keeps on existing just for the sake of the organization,
while it is less and less clear for the participants what they get out
of it. And still, they often fail to leave.
In our head such a mechanism also plays, this is how an idee fixe forms.
First there is a creative process with all kinds of ideas, where an idea
serves you and helps you forward. But after a while you start to serve
that idea, you cling to it, even if it no longer helps you. This is how
addictions are maintained: because something brought joy in the past or
worked to deal with certain situations, you keep on doing it, even if it
stopped working long ago.
Often there is thus not one source of all evil, not one leader that
caused coercion, but hierarchy comes from the whole or an aspect of the
whole. It is in the way that things are structured, that hierarchy can
emerge and be maintained.
In social power, power is exerted by the whole social fabric, instead of
one individual. It is because everyone does things a certain way, that
it is difficult to do something else. But by joining, you contribute to
this social power. Think about social norms. There are visions on power
that claim that it is always social.
There are roughly two possible kinds of interaction between a system and
its elements (or more in general between two systems): determination and
co-evolution. To explain this, letâs look to the evolution of an
organism in an ecosystem. The classical view of evolution tells that the
organism adapts to find an as fit as possible situation. Here there is
what I call determination: the individual is being influenced by the
system, while the system itself remains the same. There is thus
one-directionality.
[]
In practice there is however often co-evolution: by the acts of the
organism, the ecosystem changes. The organism is, after all, part of
that ecosystem. By running around in the âfitness-landscapeâ, the
organism changes that landscape, so that certain situations become more
or less fit than before. With co-evolution the influence thus happens in
two directions.
[] [][]
Humans are an extreme example of co-evolution, as we completely formed
our ecosystem: our culture, our technology, our social structures,...
Thatâs why the âsurvival of the fittestâ argument used by some
capitalists doesnât really hold: certain people are in this society the
âfittestâ (mainly because they happen to have a lot of money), but if we
would build another social structure, that would no longer be the case.
This difference can be spanned under our common thread. Determination
assumes after all a hierarchical structure, where a higher order system
completely determines the elements under it. There is an emphasis on
universality, searching for one main cause where everything else can be
brought under. With co-evolution however, there are cycles of mutual
influence. There is a network full of differences, where exactly these
differences bring fourth a dynamic and life. Think for example on how
many religions assume the world is created by one god, while under
scientists the idea lives that the world had formed itself through
evolution (variation and selection).
These two visions on evolution also give rise to two perspectives on how
hierarchy can disappear.
For those believing in determination, change can only happen by changing
the larger whole.
This is reflected, for example, in the Marxist view that the material
basis must first be changed to bring cultural change. Hence because
technologies and with that economic al circumstances change, the social
structure also changes.
If co-evolution is however brought up, it is also taken into account
that social structures influence technologies and economies. There is
thus a focus on that a human can indeed change something, that there is
human agency in the process, and things donât just happen behind our
back.
[]
In line with this second vision, I formulate a mechanism to avoid
hierarchy which I call constant opposition. The idea is that hierarchy
can not emerge if there is a mechanism that roots out every seed. It
thus demands constant active effort to recognize and stop hierarchy. Of
course this is still vague on how exactly it can be stopped, but
recognizing the different manifestations and not contributing to them,
but on the contrary do the opposite, is already a lot. Spreading this
practice and inspiring others do do the same, brings you even further.
Therefore, weâll go further into some general mechanisms in the
following, to apply them in a struggle against hierarchy.
---
A story:
Mechanisms to expel power in different cultures
Different authors have described mechanisms used in certain cultures to
resist hierarchy. Gelderloos argues in his âRise of Hierarchyâ [5] that
hierarchy emerges wherever there was no organization to prevent it, and
not because of certain technological or societal circumstances. This is
affirmed by the existence of hierarchical hunter-gatherer societies
(under the form of patriarchy and gerontocracy) and egalitarian
agricultural societies. Agriculture thus did not cause hierarchy, though
it did reinforce it. And the steam engine already existed in the first
century, where it was just a gadget on parties to automatically open
doors. It was only centuries later, when the social circumstances where
different, that it effectively caused an economical change[6].
An example of a mechanism used to avoid hierarchy, is found with the
Mbuti, a pretty gender-free society. They had a ritual-game to resolve
gender tensions. It started as a typical tug of war, with men and women
on opposite sides. But as soon as one side was winning, someone from the
winning team moved to the other side. At the end everyone changed gender
multiple times.
Boehm[7] also investigates mechanisms used in different egalitarian
societies to discourage hierarchical behaviour. He mentions methods
ranging from public opinion through criticism, ridicule and
disobedience, to extreme sanctions like exile and execution.
James C. Scott[8] describes communities that had social organization
that has been carved
to discourage states to annex. Actually hierarchy is contested
everywhere it emerges[9] .
The animal world also does not just let itself be determined by its
biology [10] . Chimpanzees and bonobos are biologically quite similar,
but their social organization is completely different. Bonobos are quite
peaceful, they have frequently sex as a social bonding mechanism and
females have a lot of influence. Chimpanzees, on the other hand, are
male-dominated, and aggression and domination play a large role, usually
by one alpha-male. In some primates the expelled males form homosexual
bonds that overthrow the alpha-male.
There is thus also social evolution, where individuals adapt to the
social circumstances.
---
Antifragility is a characteristic a system can meet: it is when the
system gets stronger through shocks instead of being weakened by it. Of
course the reaction of the system also depends on the nature and
strength of the shock.
Take, for example, our body: by coming into contact with germs, we
develop antibodies and can handle the illness better next time. Vaccines
are based on this principle. An expression of antifragility in social
movements is if they grow due to repression. A lot of insurrections and
revolutions start from a repressive event, for example the murder of
Alexis Grigoropoulos with the Greek riots in 2008, or a street vendor
that burns himself after police violence with the Arabic Spring.
Underlying is often a general discontent and strong social movement. But
how is antifragility possible? Therefore, we should look to a couple of
mechanisms.
Variation and selection is kinda the same principle as trial and error:
a variation of possibilities is tried out, and the best ones are
selected. Natural evolution is based on this: an organism makes
variations of itself and peers through reproduction, and those that are
best adapted to survive, will remain. This simple mechanism can thus
bring fourth a fantastic complexity.
Order from noise is a manifestation of this: this is when a more ordered
state is selected by adding variation, noise. Take, for example, a
bucket of stones where by shaking the bucket, the stones will take less
place and thus be more ordered. Antifragility can be reached in this
way: the shocks can be seen as variation, as noise, and by being exposed
to it, the system can find a better configuration. The opposite effect
is the noise from order principle. This is what happens if you try to
control everything too much. Because of this you wonât have a lot of
variation in your inputs, so that you wonât know how to deal with them
if you do get other inputs. So by sealing yourself too much, you no
longer know what to do if something does manage to penetrate your
shield. So that trying to control everything paradoxically leads to less
control.
Diversity of tactics can be linked to this principle. This is the idea
that a diversity of action methods is used, where everyone does what she
thinks is best. Nobody thus tries to convince others to all use the same
method. And exactly this combination of tactics often works better than
any method separately â in this way different fronts can be attacked at
the same time. By using a variety of tactics, it can be investigated
which one works best. Of course that is also still needed: a selection
of the methods that work, not clinging to methods. There should thus
also be enough room for criticism and discussion to improve or give up
existing methods.
In general there is always a trade-off between variation and selection
(for example in divergent versus convergent thinking): too much
variation without selection makes that good situations canât expand,
while too much selection compared to variation causes that a lot of
(possibly good) possibilities are never considered.
Positive feedback is when a deviation gets amplified. In short, when A â
B and B â A. That causes that when there is a little bit of A, B is
produced, causing more of A. In this way, there will be more and more of
A.
This is also what causes the butterfly-effect: when a small difference
brings a big effect. The classical metaphor is that the flapping of the
wings of a butterfly in Brazil can cause a tornado at the other end of
the world.
Revolutions and insurrections are often a manifestation hereof: a small
act can trigger shockwaves of bigger and bigger change, like we noted
with the Arab Spring or the Greek riots of 2008. Revolutionaries are
often looking for both the acts that trigger such cascades as the
creation of circumstances so that small deeds can grow to big changes.
But positive feedback isnât always positive. It is also the cause of the
gap between rich and poor. A small difference in income leads to a
difference in possibilities, also the possibility to earn more money. In
this way, those that already have more money, get even more, while those
who had less, get less and less (âthe rich getting richerâ effect). In
general, positive feedback is the cause of a power-law: a function where
a small portion of elements have large values, while most elements have
small values. A constant opposition can counteract such inequality, by
systematically taking only from those that have most.
A vicious circle is a manifestation from a positive feedback, for
example by being stuck in certain trains of thought, like the
alcoholic-credo: âI drink because I feel bad, and I feel bad because I
drink.â
Negative feedback, on the other hand, is when a deviation gets weakened.
In short: A â B,
B â not A. Thus, more A generates more B, but this more B induces less
of A. This brings an equilibrium, where every deviation gets brought
back to the original state. Effective repression works in this way: if
someone does something that is illegal (A), he gets punished (B), so
that he no longer dares to do it (B â not A).
But repression often doesnât work, and that is for one because a
punishment provokes discontent, so that that person will do even more
illegal things (B â A). Here there is thus a positive feedback, where
repression generates more illegal activities. Or like we noted before,
how attempting to have more control can lead to less control.
Negative feedback is what is often used to reach a goal: deviations from
a goal value are counteracted.
Neither positive nor negative feedback is therefore always good or bad,
the thing is mostly to recognize these feedbacks and stimulate or create
the wanted feedback.
The dynamics of systems can be investigated by looking which states the
system takes successively. An attractor is a set of states where the
system ends up. Once in the attractor, you canât get out: you can go to
other states within the attractor, but this will never lead to a state
outside the attractor. There can be different attractors, depending on
the starting position.
Attractors generate constraints: they make that possibilities are
confined. But you only stay within the attractor as long as the rules of
the system remain unchanged â due to a disturbance from outside, the
system can be kicked out of an attractor.
You can use this to model how a system ends up in a rigid structure, an
attractor, but also how to get out of it by constant opposition,
regularly shaking the system.
A method to coordinate without top down control or even the need to be
at the same place or time, is stigmergy. This is when traces are left in
the environment, where others build on. The origin of this concept was
to describe ants that could move very efficiently by following the
pheromones of other ants. The shorter the path, the more it can be
passed in the same amount of time, and thus the more pheromones can be
left. In this way, the shortest path is quickly found. Another example
is Wikipedia, where people successively build on an article.
Social struggles often spread through stigmergy: people are inspired by
an action they see, they learn a new method and are thus motivated to
take action themselves. We see that international (solidarity) actions
can often take place without people ever having to meet â they speak to
each other through their acts.
This is more or less the idea of propaganda of the deed, where ideas are
spread by acting accordingly. This is strongly linked to direct action,
where people act directly to change things, instead of taking detours by
for example asking the state or media for change. Goals and methods are
aligned â you do not use a method that goes against your goal or values.
Thus, the opposite of âthe goal justifies the meansâ.
All these methods and principles are closely linked and can also be
spanned under our common thread. In general, itâs about creating a sort
of ecosystem of social struggle, with cycles causing autopoiesis, so
that struggles blow back oxygen to themselves and reinforce each other.
Depending on the situation negative or positive feedback cycles can be
built in. Positive feedback so that small acts can grow to big changes.
Against every seed of power, there is, however, constant opposition â a
negative feedback. Through a broad variety of methods, the best methods
can be chosen, and these methods can reinforce each other and be
combined. With local coherence between goals, instead of considering one
goal as the most important and the rest subordinate. Coordination then
happens locally, through stigmergy.
This is also important for mental health: often there are burn-outs
because people remain stuck in actions and struggles, without having the
feeling that there is something coming out of it. We thus have to take
care that people get energy from actions, so that there is a sustainable
cycle and the energy doesnât get exhausted.
We can also find tips to fight hierarchy in other parts of this booklet.
By avoiding one-directionality, but on the contrary build in cycles and
co-evolution. By forging ties directly with individuals from all
corners, instead of going through a higher middleman. By not aiming for
universality but creating local coherence between our ideas. By
focussing on internal control over your situation, instead of always
trying to bend the world to your will. By seeing freedom as a decision,
and not as a right given to you. By focusing on what you can change as
an individual and search for this.
May these ideas inspire you to get started yourself and do your own
thing with it â because they are no more than a new beginning.
In the first place this booklet is based on my PhD thesis:
Busseniers, E. Self-organization versus hierarchical organization â a
mathematical investigation of the anarchist philosophy of social
organization. (2018).
I further refer in this booklet to a couple of works â these were not
necessarily the most important for my work, but they are those I use
most directly here.
[1] Maturana, H. R. & Varela, F. J. Autopoiesis and cognition: The
realization of the living. vol. 42 (Springer Science & Business Media,
1991).
[2] Dittrich, P. & Fenizio, P. S. di. Chemical Organisation Theory.
Bull. Math. Biol. 69, 1199â1231 (2007).
[3] Corominas-Murtra, B., Goñi, J., SolĂ©, R. V. & RodrĂguez-Caso, C. On
the origins of hierarchy in complex networks. Proc. Natl. Acad. Sci.
110, 13316â13321 (2013).
[4] BarabĂĄsi, A., DezsĆ, Z., Ravasz, E. & Oltvai, Z. Scale-free and
hierarchical structures in complex networks. SITGES Proc. COMPLEX Netw.
1--16 (2003).
[5] Gelderloos, P. The Rise of Hierarchy. (2005).
[6] Bookchin, M. History, Civilization, and Progress: Outline for a
Criticism of Modern Relativism. Green Perspect. 29, 4â5 (1994).
[7] Boehm, C. Hierarchy in the Forest: The Evolution of Egalitarian
Behavior. (Harvard University Press, 2009).
[8] Scott, J. C. The art of not being governed: An anarchist history of
upland Southeast Asia. (Yale University Press, 2009).
[9] Graeber, D. Possibilities: Essays on hierarchy, rebellion and
desire. (AK Press, 2007).
[10] Roughgarden, J. Evolutionâs rainbow: Diversity, gender, and
sexuality in nature and people. (Univ of California Press, 2013).